Mathematics In Physics Question 4
Question 4 - 2024 (29 Jan Shift 2)
A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q=\frac{a^{4} b^{3}}{c^{2}}$. The percentage error in a, b and $\mathrm{c}$ are $3 %, 4 %$ and $5 %$ respectively. Then, the percentage error in $\mathrm{Q}$ is :
(1) $66 %$
(2) $43 %$
(3) $34 %$
(4) $14 %$
Show Answer
Answer: (3)
Solution:
$\mathrm{Q}=\frac{\mathrm{a}^{4} \mathrm{~b}^{3}}{\mathrm{c}^{2}}$
$\frac{\Delta \mathrm{Q}}{\mathrm{Q}}=4 \frac{\Delta \mathrm{a}}{\mathrm{a}}+3 \frac{\Delta \mathrm{b}}{\mathrm{b}}+2 \frac{\Delta \mathrm{c}}{\mathrm{c}}$
$\frac{\Delta \mathrm{Q}}{\mathrm{Q}} \times 100=4\left(\frac{\Delta \mathrm{a}}{\mathrm{a}} \times 100\right)+3\left(\frac{\Delta \mathrm{b}}{\mathrm{b}} \times 100\right)+2\left(\frac{\Delta \mathrm{c}}{\mathrm{c}} \times 100\right)$
$$ \begin{aligned} % \text { error in } \mathrm{Q} & =4 \times 3 %+3 \times 4 %+2 \times 5 % \ & =12 %+12 %+10 % \ & =34 % \end{aligned} $$
